Hi,

I got some problems with units and normalization with the radial grating:

Lets say my grating equation is d = 1872-9459r^1+23000r^2+…where the units are in microns.

How do I insert it with the correct units to the radial graitng parameters?

edit:

I try also grating equation with d = 0.41-3.21*r^1+12.53*r^2+...in milimeters where this series is very similiar to ~1/r, still, something is wrong...

Thanks,

Nadav

Hi Nadav,

I’m not sure what you mean when you say:

something is wrong...

But this is what the Help File says about the Radial Grating:

• d is the grating spacing (always in micrometers)

• the Ai coefficients all have units of micrometers

• p is the normalized radial coordinate defined by

• where r is the radial coordinate on the surface in lens units and R is the user defined normalization radius

If your equation is already in microns, then you can just copy the coefficients into OpticStudio. I don’t know your Norm Radius and Wavelength, but I looked at your equation and found that d is roughly in the order of 1000 to 10 000 um. This means that your grating period is somewhere between 1E-3, and 1E-4 lines per um (I think the grating period is one over the grating spacing). Therefore, your diffraction angles will be quite small and hardly noticable in a 3D Layout. If I use a Norm Radius of 5.0 and use a Clear Semi-Diameter of 5.0 as well, this is what it looks at 0.55 um after 100 mm of propagation for diffraction orders +0 (blue), +1 (green), and +2 (red):

It sort of makes sense because your equation has a quadratic shape like so:

Therefore, the diffraction is closer on the optical axis because the spacing is smaller. On the edges (p = 1.0) it becomes so large that there almost isn’t any diffraction.

I hope this helps.

Take care,

David

Hi David,

Thanks for the quick and the detailed answer.

 I tried now to insert the following series: d = 1.7e2-2.97r+2.12e-2*r^2-7.7e-5*r^3+1.56e-7 *r^4-1.86e-10 *r^5+1.29e-13*r^6-4.8e-17*r^7+7.41e-21*r^8(in mircrons red in the graph)  and no matter what was the Normalziation, the grating did almost nothing. 

edit: well, it’s seems to work now.  

Thanks again,

Nadav

Hi Nadav,

When I use your equation, I get the following graph:

I’m assuming OpticStudio won’t like a negative grating spacing (d value), which is happening at about 270 um.

I’m using the following code to produce the graph:

import numpy as np
import matplotlib.pyplot as plt

# Coefficients
As =  1.7e2, -2.97, 2.12e-2, -7.7e-5, 1.56e-7, -1.86e-10, 1.29e-13, -4.8e-17, 7.41e-21]

# Grid >um]
r = np.linspace(0, 1500, 100)

# Grating spacing
d = 0

for (power, A) in enumerate(As):
    d += A * r ** power


# Plot the results
plt.figure()
plt.plot(r, d)
plt.xlabel('r aum]')
plt.ylabel('d aum]')
plt.grid()
plt.show()

This seems quite different to what you are showing, are you sure about the coefficients?

Take care,

David

Hi David,

Maybe I did mistake while copying.

Add here a new polynom that worked[ 3.47068643e-23 -2.42712129e-19  7.17714256e-16 -1.16904982e-12
  1.14551793e-09 -6.92639738e-07  2.54963018e-04 -5.39725456e-02
  6.01267046e+00]-starting with A8 and ending with A0. Now it seems to work, but I think I have now problem with our model and not with zemax. I’ll update in case I stuck again.

Thanks again for the help David,

Nadav

Hi Nadav,

My pleasure. The graph looks better with those coefficients indeed.

 Let us know if you are stuck again :)

Take care,

David